Operator Algebras and Quantum Statistical Mechanics 1
Subtitle: C*- and W*-Algebras Symmetry Groups Decomposition of States
By: by Ola Bratteli, Derek W. Robinson
Contributors: Robinson, Derek W.
Edition: Second Edition.
Series: Texts and Monographs in Physics; Texts and Monographs in Physics
Publisher: Springer Berlin Heidelberg
Published: 1987
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] :
Number of pages: 505
ISBN-13: 9783642057366; 9783662025208
Subjects: Mathematical physics; Physics
Description: This is the first of two volumes presenting the theory of operator algebras with applications to quantum statistical mechanics. The authors' approach to the operator theory is to a large extent governed by the dictates of the physical applications. The book is self-contained and most proofs are presented in detail, which makes it a useful text for students with a knowledge of basic functional analysis. The introductory chapter surveys the history and justification of algebraic techniques in statistical physics and outlines the applications that have been made. The second edition contains new and improved results. The principal changes include: A more comprehensive discussion of dissipative operators and analytic elements; the positive resolution of the question of whether maximal orthogonal probability measure on the state space of C-algebra were automatically maximal along all the probability measures on the space.
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Table of contents: title: 1. Introduction; title: 2. C-Algebras and von Neumann Algebras: C-Algebras; Representations and States; von Neumann Algebras; Tomita; title: Takesaki Modular Theory and Standard Forms of von Neumann Algebras; Quasi-Local Algebras; Miscellaneous Results and Structure; title: 3. Groups, Semigroups, and Generators: Banach Space Theory; Algebraic Theory; title: 4. Decomposition Theory: General Theory; Extremal, Central, and Subcentral Decompositions; Invariant States; Spatial Decomposition; title: References; title: List of Symbols; title: Subject Index.